| Autor: |
G. M. Tuynman, Piotr Kielanowski, Victor Buchstaber, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov |
| Rok vydání: |
2010 |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings. |
| ISSN: |
0094-243X |
| Popis: |
The philosophy of the orbit method is that there is a bijection between a class of coadjoint orbits of a given Lie group and the set of all irreducible unitary representations of that group. In order to understand what happens for Lie supergroups, we take a particular Heisenberg‐like Lie supergroup of dimension 8. For this group we decompose the regular representation into irreducible components using the Berezin‐Fourier transform. We also compute the representations associated to coadjoint orbits. It turns out that if we restrict attention to coadjoint orbits with an even symplectic form, not all irreducible components in the regular representation are recovered. Adding the coadjoint orbits with an odd symplectic form recovers some of the missing components, but not all. It is only when we consider also coadjoint orbits with a non‐homogeneous symplectic form that we recover all irreducible components appearing in the regular representation. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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